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Lovelock gravity is a class of higher-derivative gravitational theories whose linearized equations of motion have no more than two time derivatives. Here, it is shown that any Lovelock theory can be effectively described as Einstein gravity…

In this paper we extend the projective symmetry of the full metric-affine Einstein-Hilbert theory to a new symmetry transformation in the space of affine connections called the amplified symmetry. We prove that the Lagrangian of the…

In Cuzinatto et al. [Phys. Rev. D 93, 124034 (2016)], it has been demonstrated that theories of gravity in which the Lagrangian includes terms depending on the scalar curvature $R$ and its derivatives up to order $n$, i.e.…

Recently, corrections to the standard Einstein-Hilbert action are proposed to explain the current cosmic acceleration in stead of introducing dark energy. In the Palatini formulation of those modified gravity models, there is an important…

In this PhD thesis we deal with several theoretical and phenomenological apsects of metric-affine theories of gravity. Concretely, we first give a broad introduction to the necessary tools to understand the framework and elaborate on some…

There is a number of completely integrable gravity theories in two dimensions. We study the metric-affine approach on a 2-dimensional spacetime and display a new integrable model. Its properties are described and compared with the known…

In this work we study diffeomorphism-invariant metric-affine theories of gravity from the point of view of self-interacting field theories on top of Minkowski spacetime (or other background). We revise how standard metric theories couple to…

We extend the systematic calculation of an approximately relativistic Hamiltonian for centre of mass and internal dynamics of an electromagnetically bound two-particle system by Sonnleitner and Barnett [1] to the case including a weak…

Gravity is derived from an entropic action coupling matter fields with geometry. The fundamental idea is to relate the metric of Lorentzian spacetime to a quantum operator, playing the role of an renormalizable effective density matrix and…

Einstein's General Relativity (GR) is possibly one of the greatest intellectual achievements ever conceived by the human mind. In fact, over the last century, GR has proven to be an extremely successful theory, with a well established…

Alternative theories of gravity have been recently studied in connection with their cosmological applications, both in the Palatini and in the metric formalism. The aim of this paper is to propose a theoretical framework (in the Palatini…

This thesis studies modified theories of gravity from a geometric viewpoint. We review the motivations for considering alternatives to General Relativity and cover the mathematical foundations of gravitational theories in Riemannian and…

A general affine connection has enough degrees of freedom to describe the classical gravitational and electromagnetic fields in the metric-affine formulation of gravity. The gravitational field is represented in the Lagrangian by the…

We show that the new type of "non-metric" gravity theories introduced independently by Bengtsson and Krasnov can in fact be reexpressed explicitely as a metrical theory coupled to an auxiliary field. We unravel why such theories possess…

We have recently introduced a new and very simple action for three-dimensional massive gravity. This action is written in a first order formulation where the triad and the connection play a manifestly symmetric role, but where internal…

We consider gravity coupled to a second metric in the strong coupling limit, where the second kinetic term is absent. This system belongs to the recently discussed class of models of "gravity with auxiliary fields" by Pani et al. We prove…

The general relativistic treatment of gravitation can be extended by preserving the geometrical nature of the theory but modifying the form of the coupling between curvature and stress tensors. The gravitation constant is thus replaced by…

A model of Einstein-Hilbert action subject to the scale transformation is studied. By introducing a dilaton field as a means of scale transformation a new action is obtained whose Einstein field equations are consistent with traceless…

It is known that in f(R) theories of gravity with an independent connection which can be both non-metric and non symmetric, this connection can always be algebraically eliminated in favour of the metric and the matter fields, so long as it…

It is known that the metric and Palatini formalisms of gravity theories have their own interesting features but also suffer from some different drawbacks. Recently, a novel gravity theory called hybrid metric-Palatini gravity was put…